*Applied Finite Element Analysis with SolidWorks Simulation 2019*

*Applied Finite Element Analysis with SolidWorks Simulation 2019*

## Author: Cyrus Raoufi, Ph.D., P.Eng.

## ISBN: 9781-0-9919498-4-7

## Pages: 512

## Binding: Perfect Paperback

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**Description and Table of Contents:**

This textbook is intended to cover the fundamentals of the Finite Element Analysis (FEA) of mechanical components and structures using the SolidWorks Simulation^{®}. It is written primary for the engineering students, engineers, technologist and practitioners who have little or no work experience with SolidWorks Simulation. It is assumed that the readers are familiar with the fundamentals of the strength of materials as offered in an introductory level course in a typical undergraduate engineering program. However, the basic theories and formulas have been included in this text as well. This textbook can be adopted for an introductory level course in Finite Element Analysis offered to students in mechanical and civil engineering and engineering technology programs. The Direct Stiffness Method is used to develop the bar, truss, beam and frame elements. Both analytical and simulation solutions are presented through examples and tutorials to ensure that readers understand the fundamentals of FEA and the simulation software.

It is strongly recommended that readers always find a way to verify the FEA simulation results. In this textbook, the simulation results are verified for the truss, beam and frame structures using the analytical approaches through the Direct Stiffness Method. However, readers must consider that in many engineering problems, they have to deal with complicated geometries, loadings, and material properties which make it very difficult, if not impossible, to solve the problem using analytical methods.

Chapter 1 of this textbook deals mostly with the fundamentals of the mechanical loading, 3-Dimensional and 2-Dimensional stress states, four failure theories used in the SolidWorks Simulation, basics of matrix algebra, Cramer’s rule for solving linear algebraic equations, and matrix manipulation with *MATLAB ^{®}*.

Chapter 2 of this textbook presents a general overview of SolidWorks Simulation and addresses the main tools and options required in a typical FEA study. Types of analysis available in SolidWorks Simulation and four commercially available SolidWorks Simulation packages will be introduced. The three main steps in FEA include: (i) pre-processing; (ii) processing, and (iii) post-processing and are used in the SolidWorks Simulation working environment. They will be discussed in detail and related tools available in this software will be presented.

Chapter 3 of this textbook introduces several kinds of elements available in SolidWorks Simulation. The Solid Element which is used in SolidWorks Simulation to model bulky parts will be discussed in detail. The concepts of the Element Size, Aspect Ratio, and Jacobian will be discussed. Several meshing techniques available in SolidWorks Simulation such as Mesh Control, h-Adaptive, p-Adaptive, Standard Mesh with Automatic transition, and Curvature based mesh will be presented as well.

Chapter 4 of this textbook presents the Direct Stiffness Method and Truss structure analysis. The stiffness matrices will be developed for the bar and truss elements. The pre-processing, processing and post-processing tools available in SolidWorks Simulation for 1D bar element, 2D truss, and 3D truss FEA simulation will be introduced. Several examples and tutorials will be presented to show how the user can verify the simulation results by comparing them to the analytical results.

Chapter 5 of this textbook deals mostly with beam and frame analysis with SolidWorks Simulation. The stiffness matrix for a straight beam element will be developed and the Direct Stiffness Method will be used to analyze both statically determinate and indeterminate beams loaded with concentrated and distributed loads. This is done by defining their equivalent nodal forces and moments. The pre-processing, meshing and post-processing phases of a typical beam FEA with SolidWorks Simulation will be presented. As before, several examples and tutorials will be presented to show how the user can verify the simulation results by comparing them to the analytical results.

Chapter 6 of this textbook presents the application of 2D simplified and 3D shell elements available in SolidWorks Simulation. In particular, the application of 3D shell elements for analysis of thin parts such as pressure vessels and sheet metal parts will be discussed. The related pre-processing, meshing, and post-processing tools available in SolidWorks Simulation will be presented through several tutorials,

Chapter 7 of this textbook deals with assembly analysis using the contact sets. Several types of contact sets will be introduced and their application will be explored. Advanced external forces will be presented. Compatible and incompatible meshing techniques will be introduced. Beside, several techniques to simplify the simulation of assemblies will be discussed. Several examples and tutorials will be presented to show how the user can use related tools available in SolidWorks Simulation and interpret the simulation results.

Chapter 8 of this textbook introduces several types of connectors available in SolidWorks Simulation and their application. It includes the Bolt, Weld, Pin, Bearing, Spring, Elastic, Link, and Rigid connectors. Both weld and bolt connectors will be discussed in detail and several examples and tutorials will be presented.

Chapter 9 of this textbook introduces the Frequency Analysis tools provided in SolidWorks Simulation Professional to identify the natural frequencies and related mode shapes of parts and assemblies. A one degree of freedom mass-spring-damper will be presented to explain fundamental concepts such as natural frequency, mode shape, resonance, and damping ratio. The pre-processing, meshing, and post-processing tools available in SolidWorks Simulation for Frequency Analysis will be presented through several tutorials.

## Table of Contents

Chapter 1. Basic Background1-1

Mechanical Loading and Stresses1-2

Axial Loading and Normal Stress1-2

Torsional Loading and Shear Stress 1-3

Bending Moment and Normal Stress in Straight Beams 1-4

Direct Shear Loading and Shear Stress1-5

Transverse Shear Loading and Shear Stress 1-5

Linear Elastic Isotropic Model of Materials 1-7

Determining the Area (A), Moment of Inertial, and Polar Moment (J) of a Cross Section using SolidWorks1-8

3-Dimensional Principle Stresses1-10

2-Dimensional Principle Stresses 1-12

Example 1.11-14

Failure Theories1-17

Maximum von Mises Stress Criterion1-17

Maximum Shear Stress Criterion1-18

Mohr-Coulomb Stress Criterion1-18

Maximum Normal Stress Criterion 1-19

Matrix Algebra1-20

Multiplication of a Matrix by a Scalar1-20

Addition of Matrices1-20

Multiplication of Matrices1-21

Transpose of a Matrix1-21

Symmetric Matrices1-21

Unit Matrix (or Identity Matrix)1-22

Determinant of a Square Matrix1-22

Inverse of Square Matrix1-23

Orthogonal Matrix1-24

Cramer’s Rule for Solving Linear Algebraic Equations1-24

Using MATLAB to Perform Matrix Manipulation1-27

Example 1.21-28

Example 1.31-28

Example 1.41-29

Exercises1-30

Chapter 2. Fundamentals of SolidWorks Simulation2-1

Types of Analysis Available in SolidWorks Simulation Premium2-1

SolidWorks Simulation Bundles2-3

Basic Steps in FEA2-3

FEA Pre-processing2-3

FEA Processing 2-4

FEA Post-processing 2-4

Types of Elements in SolidWorks Simulation 2-6

SolidWorks Simulation Options2-6

Opening a New Simulation Study2-8

SolidWorks Simulation Working Environment2-9

Assigning Material(s) to a Part or an Assembly 2-11

Fixtures2-11

Standard Fixtures2-14

Fixed Geometry Fixture2-14

Immovable Fixture2-14

Roller/Slider Fixture2-14

Fixed Hinge 2-14

Advanced Fixture2-15

Symmetry Fixture2-15

Circular Symmetry Fixture 2-15

Use Reference Geometry Fixture2-16

On Flat Face Fixture2-16

On Cylindrical Face Fixture2-18

On Spherical Face Fixture 2-19

Structural Loads2-20

Force2-20

Uniform Force Applied Normal to a Selected Entity2-21

Torque2-22

Uniform Force Applied along a Selected Direction2-23

Nonuniform Force Applied Normal to a Selected Entity2-26

Gravity2-27

Post-processing in SolidWorks Simulation2-28

Options Available in a typical Stress Plot2-30

Edit Definition2-30

Settings2-32

Section Clipping2-33

Chart Options2-35

Probing2-36

Animating2-38

Define Factor of Safety Plot2-39

Define Design Insight Plot2-42

Define Fatigue Check Plot2-43

Generating FEA Reports2-45

Tutorial2-46

Exercise2-68

Chapter 3. Solid Element, Convergence Test and Adaptive Meshing3-1

3-Dimensional Tetrahedral Solid Element3-1

Element Size and Mesh Density3-3

Element Aspect Ratio 3-5

Jacobian Ratio3-5

Concave Element3-6

Meshing with SolidWorks Simulation 3-7

Mesh Quality Plots3-10

Convergence Check3-11

h-Adaptive Meshing3-14

p-Adaptive Meshing3-17

Mesh Control3-19

Standard Mesh with Automatic transition Selected3-22

Curvature based mesh3-22

Stress Singularity at Sharp Corners3-24

Tutorial 3.1(Mesh Refinement)3-26

Tutorial 3.2 (Stress Singularity and Mesh Control)3-34

Tutorial 3.3 (Curvature based mesh)3-38

Exercises3-44

Chapter 4. Direct Stiffness Method and Truss Analysis4-1

Direct Stiffness Method for 1-Dimensional Element4-2

Shape Functions of a 1D Spring Element4-4

Example 4.1 4-7

Pre-processing of a 1-Dimensional Structure in SolidWorks Simulation4-11

1-Dimensional Structure CAD Modeling in SolidWorks4-11

Defining a Beam Member in SolidWorks Simulation4-12

Assign the Materials to a 1-Dimensional Structure in SolidWorks Simulation4-12

Edit Joints of a 1-Dimensional Structure in SolidWorks Simulation 4-12

Apply Fixtures to the Joints of 1-Dimensional Structure in SolidWorks Simulation4-13

Apply External Loads to the Joints of a 1-Dimensional Beam Structure…………………….. 4-14

Post-processing of a 1-Dimensional Beam using the Displacement Plot4-15

Tutorial 4.14-16

Direct Stiffness Method for 2D Truss Analysis4-24

Example 4.24-28

Pre-Processing a True Structure Analysis in SolidWorks Simulation4-34

Truss CAD Modeling in SolidWorks4-34

Truss 3D Modeling in SolidWorks: Custom Profile Approach4-34

Truss 3D Modeling in SolidWorks: Structural Member Approach4-35

Truss 3D Modeling in SolidWorks: Non-Structural Approach4-36

Truss Element in SolidWorks Simulation4-37

Assign Materials to the Truss Structure in SolidWorks Simulation4-38

Edit Joints of a Truss Structure in SolidWorks Simulation4-38

Apply Fixture to the Joints of a Truss Structure in SolidWorks Simulation4-39

Apply External Loads to the Joints of a Truss Structure in SolidWorks Simulation4-41

Meshing of a Truss Structure in SolidWorks Simulation4-42

Post-Processing of a Truss Structure Analysis in SolidWorks Simulation4-42

List Axial Forces and Stresses Produced in each Truss Member4-42

Generate the Beam Diagram of the Axial Forces Produced in each Truss Member4-40

Determine the Displacements, Rotations and Reaction Forces/Moments using the Displacement Plot4-43

Tutorial 4.24-45

Direct Stiffness Method for 3D Truss Analysis4-58

Tutorial 4.34-61

Exercises4-70

Chapter 5. Beams and Frames Analysis5-1

The Direct Stiffness Method for the Beam Element5-1

Stress Components of a Beam under Axil Force, Shear Force, and Bending Moment Loading. 5-5

Normal Stress due to the Axial Loading5-5

Shear Stress at outer Layers due to the Shear Force5-5

Normal Stress due to the Bending Moment5-5

Equivalent Nodal Forces/Moments5-6

2D Planar Frames Analysis5-10

Direct Stiffness Method for 2D Planar Frame Analysis5-10

Example 5.1 5-15

Example 5.25-19

Example 5.35-22

Pre-Processing of Beams and Frames Analysis in SolidWorks Simulation5-28

Beam/Frame CAD Modeling in SolidWorks5-28

Beam Element in SolidWorks Simulation5-28

Defining the Beam Element for the Simple Beam5-28

Defining the Beam Element for a Beam Structure Made of either multi Cross-sections or multi Materials5-29

Defining the Beam Element for a frame Structure5-29

** **Assign Materials to the Beam and Frame Structure in SolidWorks Simulation5-30

Edit Joints of a Beam or Frame Structure in SolidWorks Simulation5-30

Beam Member Direction in SolidWorks Simulation5-31

Edit Beam Member Parameters in SolidWorks Simulation5-31

Beam Joint Conditions5-32

Rigid Condition at Beam Joint5-32

Hinge Condition at a Beam Joint5-32

Slide Condition at a Beam Joint5-33

Manually Specifying a Condition at a Beam Joint5-33

Beam Cross-section Properties5-34

Apply Fixtures to the Joints of a beam of Frame Structure in SolidWorks Simulation 5-35

Apply External Loads to the Joints, Points or Members of a Beam or Frame Structure 5-36

Meshing of Beam or Frame Structures in SolidWorks Simulation5-41

Post-Processing of a Beam or Frame Structure Analysis in SolidWorks Simulation5-43

List Forces and Stresses Produced in each Beam Member5-43

Generate the Beam Diagrams5-44

Determine the Displacement, Rotation and Reaction Forces/Moments using the Displacement Plot5-46

Tutorial 5.15-48

Tutorial 5.25-58

Tutorial 5.35-69

Exercises5-80

Chapter 6. 2D Simplified Elements and Thin Parts Analysis6-1

Plane Stress Element6-2

Plane Strain Element 6-3

Axisymmetric Element6-4

Pre-Processing of 2D Model of a Part in SolidWorks Simulation6-4

Defining a 2D Simplified Study6-4

Defining Fixtures for a 2D Simplified Study of a Part6-6

Defining External Loads for a 2D Simplified Study of a Part6-6

Meshing of 2D Simplified Model of a Part in SolidWorks Simulation6-8

Post-Processing of 2D Simplified Model of a Part in SolidWorks Simulation6-6

3D Shell Element in SolidWorks Simulation6-9

Modeling the Thin Parts in SolidWorks Simulation6-10

Defining the Shell Model for a Surfacebody Part using Surface Modeling Tools6-11

Defining the Shell Model for a Solidbody Part using Solid Modeling Tools6-14

Defining the Shell Model for a Sheet Metal Part6-18

Pre-Processing of 3D Shell Models of Parts in SolidWorks Simulation6-19

Pre-Processing of 3D Shell Models of Sheet Metal Parts6-19

Pre-Processing of 3D Shell Models of Surface Geometry Parts 6-19

Thin versus Thick Shell Modeling in SolidWorks Simulation6-20

Thick Shell Modeling Option for the Cylindrical Portion of the Pressure Vessel6-20

Thin Shell Modeling Option for the Cylindrical Portion of the Pressure Vessel 6-21

Thick Shell Modeling Option for the Spherical Portion of the Pressure Vessel6-21

Thin Shell Modeling Option for the Spherical Portion of the Pressure Vessel6-22

Post-Processing of 3D Shell Models of Parts in SolidWorks Simulation6-22

Shell Manager6-25

Tutorial 6.16-26

Tutorial 6.26-31

Tutorial 6.36-47

Exercises6-53

Chapter 7. Assembly Analysis with Contact Sets7-1

Centrifugal Force7-1

Bearing Load 7-2

Remote Loads/Restraints/mass7-5

Remote Mass (Rigid Connection) 7-5

Remote Loads (Rigid Connection) 7-7

Remote Loads (Direct Transfer)7-8

Remote Displacement (Rigid Connection)7-9

Distributed Mass7-10

Load Case Manager7-11

Mixed Meshing7-13

Contact Sets7-14

Contact Set Level7-14

Defining a Bonded Contact Set (Manually select contact sets)7-16

Compatible versus Incompatible Mixed Meshing7-20

Automating Bonding between Touching Entities7-21

Contact Visualization Plot7-22

Rigid Parts7-23

Excluding Parts7-23

Fix/Float Parts7-23

Incremental Meshing7-23

Tutorial 7.17-25

Exercises7-34

Chapter 8. Assembly Analysis with Connectors8-1

Edge Weld Connector Terminology8-2

Local Weld Coordinate System (WJC)8-2

Introduction to Weld Sizing Using the Elastic Vector Method 8-3

Example 8.18-4

Example 8.28-4

Example 8.38-5

Edge Weld Connector in SolidWorks Simulation8-8

Edge Weld Connector Post-Processing in SolidWorks Simulation8-9

Spot Weld Connector in SolidWorks Simulation8-11

Tutorial 8.16-12

Bolt Connector Terminology in SolidWorks Simulation8-22

Bolt Connector in SolidWorks Simulation8-23

Pin/Bolt safety check in SolidWorks Simulation8-29

Pin Connectors Terminology in SolidWorks Simulation8-31

Bearing Connectors Terminology in SolidWorks Simulation8-33

Effect of self-alignment option8-35

Flexible versus Rigid Bearing connector8-35

Spring Connectors Terminology in SolidWorks Simulation8-36

Elastic Support Connectors Terminology in SolidWorks Simulation8-38

Tutorial 8.28-39

Exercises8-49

Chapter 9. Frequency Analysis of Parts9-1

Mass-Spring-Damper System: Damped Free Vibration9-1

Mass-Spring-Damper System: Damped Forced Vibration9-3

Frequency Analysis using SolidWorks Simulation 9-5

Opening a New Frequency Analysis Study9-5

Frequency Analysis Pre-Processing9-6

Frequency Analysis Processing (Meshing and Solving)9-7

Frequency Analysis Post-Processing9-7

List the Natural Frequencies 9-7

Plot the Mode Shapes9-8

Rigid Body Modes9-10

List Mass Participation9-11

Frequency analysis of assemblies9-12

Tutorial 9.19-13

Tutorial 9.29-22

Exercises9-27